---
configs:
  - config_name: default
    data_files:
      - split: test
        path: data/test-*.parquet
  - config_name: 2d_single_loop
    data_files:
      - split: test
        path: data/2d_single_loop/test-*.parquet
  - config_name: 2d_maze_loop
    data_files:
      - split: test
        path: data/2d_maze_loop/test-*.parquet
---

# OrdinalBench

**OrdinalBench** is a synthetic benchmark for evaluating ordinal reasoning capabilities of vision-language models (VLMs). It tests whether models can correctly identify the N-th element along structured visual paths — circular loops and maze traversals — in 2D top-down scenes.

🌐 **Project page:** [ordinalbench.github.io](https://ordinalbench.github.io)
🔧 **Evaluation toolkit:** [github.com/ordinalbench/ordinalbench-public](https://github.com/ordinalbench/ordinalbench-public)
📦 **Dataset:** [huggingface.co/datasets/u-lec16/ordinalbench-dataset](https://huggingface.co/datasets/u-lec16/ordinalbench-dataset)

## Dataset Summary

| Variant | Modality | Images | QA Pairs | Description |
|---|---|---|---|---|
| `2d_single_loop` | 2D top-down | 1,000 | 15,000 | Count along circular arrangements of labeled objects |
| `2d_maze_loop` | 2D top-down | 1,000 | 15,000 | Traverse maze corridors following turn-preference rules |
| **Total** | — | **2,000** | **30,000** | — |

### Difficulty Axes

- **Ordinal Level (N magnitude):** Within Objects (N ≤ total objects), Exceed Objects (N > total objects, ≤ 99), Large Scale (100 ≤ N ≤ 300)
- **Object Count / Grid Size:** Few (5 / 7×7), Medium (10 / 11×11), Many (20 / 21×21)
- **Stride:** 1 (every step), 2 (skip-1), 3 (skip-2)

## Usage

### With 🤗 Datasets

```python
from datasets import load_dataset

# Load all variants
ds = load_dataset("u-lec16/ordinalbench-dataset")

# Load a specific variant
ds_maze = load_dataset("u-lec16/ordinalbench-dataset", "2d_maze_loop")

# Inspect a sample
sample = ds_maze["test"][0]
print(sample["question"])
print(sample["answer"])
sample["image"].show()  # PIL Image
```

### With the Evaluation Toolkit

```bash
pip install ordinalbench  # or: uv sync
ob run --model openai --input <annotation.jsonl> --images-dir <images/> --output predictions.jsonl
ob score --preds predictions.jsonl --truth <annotation.jsonl>
```

## Annotation Schema

Each record contains:

| Field | Type | Description |
|---|---|---|
| `question_id` | str | Unique question identifier |
| `image` | Image | The input image |
| `question` | str | Natural language instruction |
| `answer` | str | Ground-truth identifier |
| `N` | int | Target ordinal position (1-indexed, up to 300) |
| `ordinal_level` | str | `Within Objects` / `Exceed Objects` / `Large Scale` |
| `stride` | int | Counting stride (1, 2, or 3) |
| `modality` | str | `2d` |
| `loop_type` | str | `single` or `maze` |
| `trace` | list | Step-by-step traversal trace |

## Data Splits

Currently provides a single `test` split designed for zero-shot evaluation. Training splits can be generated using the toolkit's data generation pipelines.

## Limitations

- Synthetic data — limited real-world visual noise and lighting variation
- Questions are in English only
- Large Scale (N up to 300) may exceed token limits of some models

## Citation

```bibtex
@article{ordinalbench2025,
  title={OrdinalBench: A Benchmark for Ordinal Reasoning in Vision-Language Models},
  author={Tozaki, Yusuke},
  year={2025}
}
```

## License

MIT